Mathematics: Which function s graph has asymptotes located at the values x=pi/2+-npi? 1. y = sin x2. y = sec x3. y = cot x4. y = tan x a) 2 onlyb) 1 onlyc) 1 and 3 onlyd) 2 and 4 only

ASA congruence theorem: If two angles and the included side of one triangle are equal to the corresponding angles and side of another triangle, the triangles are congruent.Step-by-step explanation:I just did that one...

Which function s graph has asymptotes located at

Ответ:

ssrt8771

14.03.2022

Mathematics

Option 2 and 4

Step-by-step explanation:

Given : Function's graph has asymptotes located at the values $x=\frac{\pi}{2}\pm n\pi$

To find : Which function graph has asymptote given?

Solution :

An asymptote is a line or curve that approaches a given curve.

To find vertical asymptote the limit has to go to either ∞ or − ∞ , which happens when the denominator becomes zero.

The sine are defined for all real x, y is defined for all real x, so there are no vertical asymptotes.

So, Option 1 is not true.

In option 3,

$y=\cot x=\frac{\cos x}{\sin x}$

When we put Denominator = 0

$\sin x=0$

Value of x lie between $(0,n\pi)$

So, Option 3 is not true.

In Option 2,

$y=\sec x=\frac{1}{\cos x}$

When we put Denominator = 0

$\cos x=0$

When cos x=0 the values of x is

$x=\pm\frac{\pi}{2},\pm\frac{3\pi}{2},\pm\frac{5\pi}{2},.....$

$x=\frac{\pi}{2}\pm n\pi$

Therefore, The graph of y= sec x has asymptote located at the values $x=\frac{\pi}{2}\pm n\pi$

So, Option 2 is correct.

In Option 4,

$y=\tan x=\frac{sin x}{\cos x}$

When we put Denominator = 0

$\cos x=0$

When cos x=0 the values of x is

$x=\pm\frac{\pi}{2},\pm\frac{3\pi}{2},\pm\frac{5\pi}{2},.....$

$x=\frac{\pi}{2}\pm n\pi$

Therefore, The graph of y= tan x has asymptote located at the values $x=\frac{\pi}{2}\pm n\pi$

So, Option 4 is correct.

Therefore, Option 2 and 4 are correct.

Hence Option A is correct - 2 only

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Which function's graph has asymptotes located at the values x=pi/2+-npi? 1. y = sin x2. y = sec x3. y = cot x4. y = tan x a) 2 onlyb) 1 onlyc) 1 and 3 onlyd) 2 and 4 only

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